It depends on the business needs. Usually I would stay away from using triggers for that, as this is a business logic, and should be handled by the BL.
But the answer is Yes to your question - you can do that, just make sure to call the web service asynchronously, so it does not delay the insert while the web service call finishes.
You may also consider using OneWay web service - i.e. fire and forget.
But, as others pointed out - you are always better off not using trigger.
If properly architectured, there should be only one piece of code, which can communicate with the database, i.e. some abstraction of the DAL in only a single service. Hook there to make whatever is needed after an insert.
I would go with a trigger, if there are many different applications which can write in the database with a direct access to the database, not trough a DAL service. Which again is a disaster waiting to happen.
Another situation, in which I may go with a trigger, if I have to deal with internally hosted third party application, i.e. if I have access to the database server itself, but not to the code which writes in the database.